This introductory text on partial differential equations is the first to integrate modern and classical techniques for solving PDEs at a level suitable for undergraduates. The author successfully complements the classical topic of Fourier series with modern finite element methods. The result is an up-to-date, powerful, and flexible approach to solving PDEs, which both faculty and students will find refreshing, challenging, and rewarding.
Linear algebra is a key component of the text, providing a framework both for computing solutions and for understanding the theoretical basis of the methods. Although techniques are emphasized over theory, the methods are presented in a mathematically sound fashion to develop a strong foundation for further study. Numerous exercises and examples involve meaningful experiments with realistic physical parameters, allowing students to use physical intuition to understand the qualitative features of the solutions.
A modern course in PDEs at this level calls for the use of powerful software. Although the text is independent of any particular software package, the accompanying CD-ROM includes thorough tutorials on using Matlab, Mathematica, and Maple to compute and graph solutions.
The subject of partial differential equations is among the most difficult subjects to teach. Partial Differential Equations: Analytical and Numerical Methods has many features to ease the student into the subject:
- thorough expositions of the background material from linear algebra and ordinary differential equations;
- an emphasis on connecting mathematical results with physical understanding;
- some of the best tutorial material available for Matlab, Mathematica, and Maple;
- solutions to odd-numbered exercises, including, in many cases, a complete outline of the solution process.
